Problem: Which of the following numbers is a multiple of 13? ${45,63,78,111,114}$
Explanation: The multiples of $13$ are $13$ $26$ $39$ $52$ ..... In general, any number that leaves no remainder when divided by $13$ is considered a multiple of $13$ We can start by dividing each of our answer choices by $13$ $45 \div 13 = 3\text{ R }6$ $63 \div 13 = 4\text{ R }11$ $78 \div 13 = 6$ $111 \div 13 = 8\text{ R }7$ $114 \div 13 = 8\text{ R }10$ The only answer choice that leaves no remainder after the division is $78$ $ 6$ $13$ $78$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $13$ are contained within the prime factors of $78$ $78 = 2\times3\times13 13 = 13$ Therefore the only multiple of $13$ out of our choices is $78$. We can say that $78$ is divisible by $13$.